The computation of the periodogram is performed with zero-padding [1]}, i.e. zeros are added at the end of the sample resulting in a new sample \((x(1),\dots ,x(n),0,\dots ,0)\)  of length \(\tilde{n}>n\) . Hence, the discrete Fourier transform is computed on a finer grid \(\left\lbrace 2\pi j/\tilde{n}\right\rbrace _{j=1}^{\tilde{n}}\)  resulting in an interpolation of the periodogram between the actual Fourier frequencies \(\left\lbrace 2\pi j/n\right\rbrace _{j=1}^n\) , which allows us to better distinguish between peaks. Zero-padding has no noticable effect on the computation time of the periodogram estimate. It is practical to choose \(\tilde{n}\)  to be a power of 2 to make use of the (Cooley-Tukey or radix-2) fast Fourier transform and its reduced complexity of \(O(\tilde{n}\log \tilde{n})\)  compared to the direct computation of the discrete Fourier transform [1]}.
For our examples the samples were zero-padded with \(\tilde{n}=2^{13}=8192\) .
